A behavioural model for vague probability assessments

I present an hierarchical uncertainty model that is able to represent vague probability assessments, and to make inferences based on them. This model can be given an interpretation in terms of the behaviour of a modeller in the face of uncertainty, and is based on Walley’s theory of imprecise probabilities. It is formally closely related to Zadeh’s fuzzy probabilities, but it has a different interpretation, and a different calculus. Through rationality (coherence) arguments, the hierarchical model is shown to lead to an imprecise first-order uncertainty model that can be used in decision making, and as a prior in statistical reasoning.